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Dominique Lord - One of the best experts on this subject based on the ideXlab platform.
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modeling over dispersed crash data with a long tail examining the accuracy of the Dispersion Parameter in negative binomial models
Analytic Methods in Accident Research, 2015Co-Authors: Lingtao Wu, Dominique LordAbstract:Despite many statistical models that have been proposed for modeling motor vehicle crashes, the most commonly used statistical tool remains the Negative Binomial (NB) model. Crash data collected for safety studies may exhibit over-Dispersion and a long tail (i.e., a few sites have unusually high number of crashes). However, some studies have shown that NB models cannot handle over-dispersed count data with a long tail adequately. So far, no work has investigated the performance of the Dispersion Parameter of the NB model when analyzing over-dispersed crash data with a long tail. The Dispersion Parameter of the NB model plays an important role in various types of transportation safety analysis. The first objective of this study is to examine whether the Dispersion Parameter can truly reflect the level of Dispersion in over-dispersed crash data with a long tail. The second objective is to determine whether the Dispersion term of the Sichel (SI) model can be used as an alternative to the Dispersion Parameter of the NB model. To accomplish the objectives of this study, crash data sets are simulated from NB and SI regression models using different values describing the mean and the Dispersion level. For the simulated data sets, the Dispersion Parameter and Dispersion term are estimated and compared to the true values. To complement the output of the simulation study, crash data collected in Texas are also used to compare the Dispersion Parameter and Dispersion term. The results from this study suggest that the Dispersion Parameter of the NB model can erroneously estimate the level of Dispersion in over-dispersed count data with a long tail and the Dispersion term of the SI model is more reliable in estimating the true level of Dispersion. Thus, considering the findings in this study, it is believed that the Dispersion term may offer a viable alternative for analyzing over-dispersed crash data with a long tail.
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bias properties of bayesian statistics in finite mixture of negative binomial regression models in crash data analysis
Accident Analysis & Prevention, 2010Co-Authors: Byungjung Park, Dominique Lord, Jeffrey D HartAbstract:Factors that cause heterogeneity in crash data are often unknown to researchers and failure to accommodate such heterogeneity in statistical models can undermine the validity of empirical results. A recently proposed finite mixture for the negative binomial regression model has shown a potential advantage in addressing the unobserved heterogeneity as well as providing useful information about features of the population under study. Despite its usefulness, however, no study has been found to examine the performance of this finite mixture under various conditions of sample sizes and sample-mean values that are common in crash data analysis. This study investigated the bias associated with the Bayesian summary statistics (posterior mean and median) of Dispersion Parameters in the two-component finite mixture of negative binomial regression models. A simulation study was conducted using various sample sizes under different sample-mean values. Two prior specifications (non-informative and weakly-informative) on the Dispersion Parameter were also compared. The results showed that the posterior mean using the non-informative prior exhibited a high bias for the Dispersion Parameter and should be avoided when the dataset contains less than 2,000 observations (even for high sample-mean values). The posterior median showed much better bias properties, particularly at small sample sizes and small sample means. However, as the sample size increases, the posterior median using the non-informative prior also began to exhibit an upward-bias trend. In such cases, the posterior mean or median with the weakly-informative prior provided smaller bias. Based on simulation results, guidelines about the choice of priors and the summary statistics to use are presented for different sample sizes and sample-mean values.
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analyzing different Parameterizations of the varying Dispersion Parameter as a function of segment length
Transportation Research Record, 2009Co-Authors: Srinivas Reddy Geedipally, Dominique Lord, Byungjung ParkAbstract:Until a few years ago, the Dispersion Parameter of Poisson-gamma models had been assumed to be invariant of the characteristics of the observations under study, but recent research in highway safety has shown that the Dispersion Parameter can depend on the covariates of the model. To account for this dependence, some researchers have reported that the Dispersion Parameter should be modeled solely as a function of segment length. The primary objective of this research was to examine empirically whether the Dispersion Parameter should be characterized using only the length of the segment. If not, the secondary objective consisted of determining alternative Parameterizations using other covariates that would offer a better approach for characterizing the variance function of Poisson-gamma models. To accomplish the study objectives, 10 Parameterizations describing the varying Dispersion Parameter were estimated with three different data sets collected in Texas, California, and Washington State. Flow-only models were used for comparing the Parameterizations. The Akaike information criterion and other related goodness-of-fit (GOF) measures were used for evaluating and comparing the different models. The results of this study show that no single functional form or Parameterization is suitable for all the data sets. Traffic flow was more significantly associated with the structured variation observed in the data than segment length. It is therefore recommended that transportation safety analysts evaluate different Parameterizations and select the most appropriate one using a combination of GOF criteria, including the significance of the model's coefficients.
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examining application of aggregated and disaggregated poisson gamma models subjected to low sample mean bias
Transportation Research Record, 2009Co-Authors: Dominique Lord, Maneesh MahlawatAbstract:Two general classes of models have been proposed for modeling crash data: disaggregated (both with and without time trend) and aggregated models. Poisson-gamma models have traditionally been used under both of these model classes. As documented in previous studies, data sets characterized by small sample size and low mean values can significantly affect the performance of Poisson-gamma models, particularly those related to the estimation of the inverse Dispersion Parameter. Thus, guidance is needed on when to use aggregated models instead of disaggregated models as a function of the sample size and the sample mean value. The objective of this study was to estimate the conditions in which aggregated models (with a higher mean but a smaller sample size) could provide a more reliable estimate of the inverse Dispersion Parameter than disaggregated models (with a lower sample mean value but a larger sample size) or vice versa. To accomplish this objective, several simulation runs were performed for different v...
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adjustment for maximum likelihood estimate of negative binomial Dispersion Parameter
Transportation Research Record, 2008Co-Authors: Byungjung Park, Dominique LordAbstract:The negative binomial (NB) (or Poisson-gamma) model has been used extensively by highway safety analysts because it can accommodate the overDispersion often exhibited in crash data. However, it has been reported in the literature that the maximum likelihood estimate of the Dispersion Parameter of NB models can be significantly affected when the data are characterized by small sample size and low sample mean. Given the important roles of the Dispersion Parameter in various types of highway safety analyses, there is a need to determine whether the bias could be potentially corrected or minimized. The objectives of this study are to explore whether a systematic relationship exists between the estimated and true Dispersion Parameters, determine the bias as a function of the sample size and sample mean, and develop a procedure for correcting the bias caused by these two conditions. For this purpose, simulated data were used to derive the relationship under the various combinations of sample mean, Dispersion pa...
Alex Alvarado - One of the best experts on this subject based on the ideXlab platform.
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frequency logarithmic perturbation on the group velocity Dispersion Parameter with applications to passive optical networks
Journal of Lightwave Technology, 2021Co-Authors: Vinicius Oliari, Erik Agrell, Gabriele Liga, Alex AlvaradoAbstract:Signal propagation in an optical fiber can be described by the nonlinear Schr\"odinger equation (NLSE). The NLSE has no known closed-form solution, mostly due to the interaction of Dispersion and nonlinearities. In this paper, we present a novel closed-form approximate model for the nonlinear optical channel, with applications to passive optical networks. The proposed model is derived using logarithmic perturbation in the frequency domain on the group-velocity Dispersion (GVD) Parameter of the NLSE. The model can be seen as an improvement of the recently proposed regular perturbation (RP) on the GVD Parameter. RP and logarithmic perturbation (LP) on the nonlinear coefficient have already been studied in the literature, and are hereby compared with RP on the GVD Parameter and the proposed LP model. As an application of the model, we focus on passive optical networks. For a 20 km PON at 10 Gbaud, the proposed model improves upon LP on the nonlinear coefficient by 1.5 dB. For the same system, a detector based on the proposed LP model reduces the uncoded bit-error-rate by up to 5.4 times at the same input power or reduces the input power by 0.4 dB at the same information rate.
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regular perturbation on the group velocity Dispersion Parameter for nonlinear fibre optical communications
Nature Communications, 2020Co-Authors: Vinicius Oliari, Erik Agrell, Alex AlvaradoAbstract:Communication using the optical fibre channel can be challenging due to nonlinear effects that arise in the optical propagation. These effects represent physical processes that originate from light propagation in optical fibres. To obtain fundamental understandings of these processes, mathematical models are typically used. These models are based on approximations of the nonlinear Schrodinger equation, the differential equation that governs the propagation in an optical fibre. All available models in the literature are restricted to certain regimes of operation. Here, we present an approximate model for the nonlinear optical fibre channel in the weak-Dispersion regime, in a noiseless scenario. The approximation is obtained by applying regular perturbation theory on the group-velocity Dispersion Parameter of the nonlinear Schrodinger equation. The proposed model is compared with three other models using the normalized square deviation metric and shown to be significantly more accurate for links with high nonlinearities and weak Dispersion.
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regular perturbation on the group velocity Dispersion Parameter for nonlinear fibre optical communications
Nature Communications, 2020Co-Authors: Vinicius Oliari, Erik Agrell, Alex AlvaradoAbstract:Communication using the optical fibre channel can be challenging due to nonlinear effects that arise in the optical propagation. These effects represent physical processes that originate from light propagation in optical fibres. To obtain fundamental understandings of these processes, mathematical models are typically used. These models are based on approximations of the nonlinear Schrodinger equation, the differential equation that governs the propagation in an optical fibre. All available models in the literature are restricted to certain regimes of operation. Here, we present an approximate model for the nonlinear optical fibre channel in the weak-Dispersion regime, in a noiseless scenario. The approximation is obtained by applying regular perturbation theory on the group-velocity Dispersion Parameter of the nonlinear Schrodinger equation. The proposed model is compared with three other models using the normalized square deviation metric and shown to be significantly more accurate for links with high nonlinearities and weak Dispersion. Nonlinear effects have been studied in optical fiber communications channels under various specified Parameter regimes. Here, the authors develop an approximate model via perturbation that is more accurate for the highly nonlinear regime.
James O Lloydsmith - One of the best experts on this subject based on the ideXlab platform.
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inference of r0 and transmission heterogeneity from the size distribution of stuttering chains
PLOS Computational Biology, 2013Co-Authors: James O Lloydsmith, Seth BlumbergAbstract:For many infectious disease processes such as emerging zoonoses and vaccine-preventable diseases, and infections occur as self-limited stuttering transmission chains. A mechanistic understanding of transmission is essential for characterizing the risk of emerging diseases and monitoring spatio-temporal dynamics. Thus methods for inferring and the degree of heterogeneity in transmission from stuttering chain data have important applications in disease surveillance and management. Previous researchers have used chain size distributions to infer , but estimation of the degree of individual-level variation in infectiousness (as quantified by the Dispersion Parameter, ) has typically required contact tracing data. Utilizing branching process theory along with a negative binomial offspring distribution, we demonstrate how maximum likelihood estimation can be applied to chain size data to infer both and the Dispersion Parameter that characterizes heterogeneity. While the maximum likelihood value for is a simple function of the average chain size, the associated confidence intervals are dependent on the inferred degree of transmission heterogeneity. As demonstrated for monkeypox data from the Democratic Republic of Congo, this impacts when a statistically significant change in is detectable. In addition, by allowing for superspreading events, inference of shifts the threshold above which a transmission chain should be considered anomalously large for a given value of (thus reducing the probability of false alarms about pathogen adaptation). Our analysis of monkeypox also clarifies the various ways that imperfect observation can impact inference of transmission Parameters, and highlights the need to quantitatively evaluate whether observation is likely to significantly bias results.
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maximum likelihood estimation of the negative binomial Dispersion Parameter for highly overdispersed data with applications to infectious diseases
PLOS ONE, 2007Co-Authors: James O LloydsmithAbstract:Background The negative binomial distribution is used commonly throughout biology as a model for overdispersed count data, with attention focused on the negative binomial Dispersion Parameter, k. A substantial literature exists on the estimation of k, but most attention has focused on datasets that are not highly overdispersed (i.e., those with k≥1), and the accuracy of confidence intervals estimated for k is typically not explored. Methodology This article presents a simulation study exploring the bias, precision, and confidence interval coverage of maximum-likelihood estimates of k from highly overdispersed distributions. In addition to exploring small-sample bias on negative binomial estimates, the study addresses estimation from datasets influenced by two types of event under-counting, and from disease transmission data subject to selection bias for successful outbreaks. Conclusions Results show that maximum likelihood estimates of k can be biased upward by small sample size or under-reporting of zero-class events, but are not biased downward by any of the factors considered. Confidence intervals estimated from the asymptotic sampling variance tend to exhibit coverage below the nominal level, with overestimates of k comprising the great majority of coverage errors. Estimation from outbreak datasets does not increase the bias of k estimates, but can add significant upward bias to estimates of the mean. Because k varies inversely with the degree of overDispersion, these findings show that overestimation of the degree of overDispersion is very rare for these datasets.
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maximum likelihood estimation of the negative binomial Dispersion Parameter for highly overdispersed data with applications to infectious diseases
PLOS ONE, 2007Co-Authors: James O LloydsmithAbstract:Author(s): Lloyd-Smith, James O | Abstract: BackgroundThe negative binomial distribution is used commonly throughout biology as a model for overdispersed count data, with attention focused on the negative binomial Dispersion Parameter, k. A substantial literature exists on the estimation of k, but most attention has focused on datasets that are not highly overdispersed (i.e., those with kgor=1), and the accuracy of confidence intervals estimated for k is typically not explored.MethodologyThis article presents a simulation study exploring the bias, precision, and confidence interval coverage of maximum-likelihood estimates of k from highly overdispersed distributions. In addition to exploring small-sample bias on negative binomial estimates, the study addresses estimation from datasets influenced by two types of event under-counting, and from disease transmission data subject to selection bias for successful outbreaks.ConclusionsResults show that maximum likelihood estimates of k can be biased upward by small sample size or under-reporting of zero-class events, but are not biased downward by any of the factors considered. Confidence intervals estimated from the asymptotic sampling variance tend to exhibit coverage below the nominal level, with overestimates of k comprising the great majority of coverage errors. Estimation from outbreak datasets does not increase the bias of k estimates, but can add significant upward bias to estimates of the mean. Because k varies inversely with the degree of overDispersion, these findings show that overestimation of the degree of overDispersion is very rare for these datasets.
Vinicius Oliari - One of the best experts on this subject based on the ideXlab platform.
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frequency logarithmic perturbation on the group velocity Dispersion Parameter with applications to passive optical networks
Journal of Lightwave Technology, 2021Co-Authors: Vinicius Oliari, Erik Agrell, Gabriele Liga, Alex AlvaradoAbstract:Signal propagation in an optical fiber can be described by the nonlinear Schr\"odinger equation (NLSE). The NLSE has no known closed-form solution, mostly due to the interaction of Dispersion and nonlinearities. In this paper, we present a novel closed-form approximate model for the nonlinear optical channel, with applications to passive optical networks. The proposed model is derived using logarithmic perturbation in the frequency domain on the group-velocity Dispersion (GVD) Parameter of the NLSE. The model can be seen as an improvement of the recently proposed regular perturbation (RP) on the GVD Parameter. RP and logarithmic perturbation (LP) on the nonlinear coefficient have already been studied in the literature, and are hereby compared with RP on the GVD Parameter and the proposed LP model. As an application of the model, we focus on passive optical networks. For a 20 km PON at 10 Gbaud, the proposed model improves upon LP on the nonlinear coefficient by 1.5 dB. For the same system, a detector based on the proposed LP model reduces the uncoded bit-error-rate by up to 5.4 times at the same input power or reduces the input power by 0.4 dB at the same information rate.
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regular perturbation on the group velocity Dispersion Parameter for nonlinear fibre optical communications
Nature Communications, 2020Co-Authors: Vinicius Oliari, Erik Agrell, Alex AlvaradoAbstract:Communication using the optical fibre channel can be challenging due to nonlinear effects that arise in the optical propagation. These effects represent physical processes that originate from light propagation in optical fibres. To obtain fundamental understandings of these processes, mathematical models are typically used. These models are based on approximations of the nonlinear Schrodinger equation, the differential equation that governs the propagation in an optical fibre. All available models in the literature are restricted to certain regimes of operation. Here, we present an approximate model for the nonlinear optical fibre channel in the weak-Dispersion regime, in a noiseless scenario. The approximation is obtained by applying regular perturbation theory on the group-velocity Dispersion Parameter of the nonlinear Schrodinger equation. The proposed model is compared with three other models using the normalized square deviation metric and shown to be significantly more accurate for links with high nonlinearities and weak Dispersion.
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regular perturbation on the group velocity Dispersion Parameter for nonlinear fibre optical communications
Nature Communications, 2020Co-Authors: Vinicius Oliari, Erik Agrell, Alex AlvaradoAbstract:Communication using the optical fibre channel can be challenging due to nonlinear effects that arise in the optical propagation. These effects represent physical processes that originate from light propagation in optical fibres. To obtain fundamental understandings of these processes, mathematical models are typically used. These models are based on approximations of the nonlinear Schrodinger equation, the differential equation that governs the propagation in an optical fibre. All available models in the literature are restricted to certain regimes of operation. Here, we present an approximate model for the nonlinear optical fibre channel in the weak-Dispersion regime, in a noiseless scenario. The approximation is obtained by applying regular perturbation theory on the group-velocity Dispersion Parameter of the nonlinear Schrodinger equation. The proposed model is compared with three other models using the normalized square deviation metric and shown to be significantly more accurate for links with high nonlinearities and weak Dispersion. Nonlinear effects have been studied in optical fiber communications channels under various specified Parameter regimes. Here, the authors develop an approximate model via perturbation that is more accurate for the highly nonlinear regime.
Byungjung Park - One of the best experts on this subject based on the ideXlab platform.
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bias properties of bayesian statistics in finite mixture of negative binomial regression models in crash data analysis
Accident Analysis & Prevention, 2010Co-Authors: Byungjung Park, Dominique Lord, Jeffrey D HartAbstract:Factors that cause heterogeneity in crash data are often unknown to researchers and failure to accommodate such heterogeneity in statistical models can undermine the validity of empirical results. A recently proposed finite mixture for the negative binomial regression model has shown a potential advantage in addressing the unobserved heterogeneity as well as providing useful information about features of the population under study. Despite its usefulness, however, no study has been found to examine the performance of this finite mixture under various conditions of sample sizes and sample-mean values that are common in crash data analysis. This study investigated the bias associated with the Bayesian summary statistics (posterior mean and median) of Dispersion Parameters in the two-component finite mixture of negative binomial regression models. A simulation study was conducted using various sample sizes under different sample-mean values. Two prior specifications (non-informative and weakly-informative) on the Dispersion Parameter were also compared. The results showed that the posterior mean using the non-informative prior exhibited a high bias for the Dispersion Parameter and should be avoided when the dataset contains less than 2,000 observations (even for high sample-mean values). The posterior median showed much better bias properties, particularly at small sample sizes and small sample means. However, as the sample size increases, the posterior median using the non-informative prior also began to exhibit an upward-bias trend. In such cases, the posterior mean or median with the weakly-informative prior provided smaller bias. Based on simulation results, guidelines about the choice of priors and the summary statistics to use are presented for different sample sizes and sample-mean values.
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analyzing different Parameterizations of the varying Dispersion Parameter as a function of segment length
Transportation Research Record, 2009Co-Authors: Srinivas Reddy Geedipally, Dominique Lord, Byungjung ParkAbstract:Until a few years ago, the Dispersion Parameter of Poisson-gamma models had been assumed to be invariant of the characteristics of the observations under study, but recent research in highway safety has shown that the Dispersion Parameter can depend on the covariates of the model. To account for this dependence, some researchers have reported that the Dispersion Parameter should be modeled solely as a function of segment length. The primary objective of this research was to examine empirically whether the Dispersion Parameter should be characterized using only the length of the segment. If not, the secondary objective consisted of determining alternative Parameterizations using other covariates that would offer a better approach for characterizing the variance function of Poisson-gamma models. To accomplish the study objectives, 10 Parameterizations describing the varying Dispersion Parameter were estimated with three different data sets collected in Texas, California, and Washington State. Flow-only models were used for comparing the Parameterizations. The Akaike information criterion and other related goodness-of-fit (GOF) measures were used for evaluating and comparing the different models. The results of this study show that no single functional form or Parameterization is suitable for all the data sets. Traffic flow was more significantly associated with the structured variation observed in the data than segment length. It is therefore recommended that transportation safety analysts evaluate different Parameterizations and select the most appropriate one using a combination of GOF criteria, including the significance of the model's coefficients.
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adjustment for maximum likelihood estimate of negative binomial Dispersion Parameter
Transportation Research Record, 2008Co-Authors: Byungjung Park, Dominique LordAbstract:The negative binomial (NB) (or Poisson-gamma) model has been used extensively by highway safety analysts because it can accommodate the overDispersion often exhibited in crash data. However, it has been reported in the literature that the maximum likelihood estimate of the Dispersion Parameter of NB models can be significantly affected when the data are characterized by small sample size and low sample mean. Given the important roles of the Dispersion Parameter in various types of highway safety analyses, there is a need to determine whether the bias could be potentially corrected or minimized. The objectives of this study are to explore whether a systematic relationship exists between the estimated and true Dispersion Parameters, determine the bias as a function of the sample size and sample mean, and develop a procedure for correcting the bias caused by these two conditions. For this purpose, simulated data were used to derive the relationship under the various combinations of sample mean, Dispersion pa...